Question

In the figure, the potentiometer wire $AB$ of length $L$ and resistnace $9r$ is joined to the cell $D$ of e.m.f and internal resistance $r$. The cell $C$'s emf is $\epsilon /2$ and its internal resistance is $2r$.
The galvanometer $G$ will show no deflection when the length $AJ$ is

• A. $4L/9$
• B. $5L/9$
• C. $7L/18$
• D. $11L/18$

Answer 1

The correct option is B $5L/9$

Current through potentiometer $=\frac{\epsilon }{r+9r}=\frac{\epsilon }{10r}$

Potential difference across potentiometer = i $\times$ 9r = V

$=\frac{\epsilon }{10r}\times 9r=V\frac{9\epsilon }{10}=V$

Potential gradient $\frac{V}{L}=\frac{9\epsilon }{10L}$ =K

For no deflection

$\frac{\epsilon }{2}=k\left(AJ\right)\frac{\epsilon }{2}=\frac{9\epsilon }{10L}\times AJ$

AJ $=\frac{5}{9}L$